In the case of the \((as)\)  fermions, we construct link variable \(U^{(as)}_\mu (x)\) ,
and thus the Dirac operator \(D^{(as)}_m\) , by following the prescription in Ref. [1]}.
We first define an orthonormal basis \(e_{(as)}^{(ab)}\)  (the multi-index \((ab)\)  runs
over ordered pairs with \(1 \le a < b \le 2N\) )
for the appropriate vector space of
\(2N\times 2N\)  antisymmetric (and \(\Omega \) -traceless) matrices.
There are \(N(2N-1)-1\)  such matrices.
For \(b=N+a\)  and \(2\le a\le N\) , they have the following non-vanishing entries:
\((e_{(as)}^{(ab)})_{c,N+c}\equiv -(e_{(as)}^{(ab)})_{N+c,c}\equiv \left\lbrace \begin{matrix}&\frac{1}{\sqrt{2\,a\,(a-1)}},~~~\textrm {for}~c<a,\\&\frac{-(a-1)}{\sqrt{2\,a\,(a-1)}},~~~\textrm {for}~c=a,\\\end{matrix}\right.\) 
